In a right triangle one of the legs is 3 cm smaller than the hypotenuse, and the other leg is 6 cm smaller than the hypotenuse.

Question

Find the length of the hypotenuse.

 

 

I have a quiz on this in one hour. PLease help me!!

Answer 1

Let x = the length of the hypotenuse, then use the Pythagorean Theorem:

 

(x-3)² + (x-6)² = x²

 

x² - 6x + 6 + x² - 12x + 36 = x²

x² - 18x + 45 = 0

(x-15)(x-3) = 0

 

x = 15 and 3

 

x cannot equal 3 because the sides are:

 

x - 3 = 3 - 3 = 0

x - 6 = 3 - 6 = -3

 

You can't have a triangle with sides = 0 and -3. So the answer is x = 15 cm (sides are 12 and 9 cm).

Answer 2

h=hypotenuse

h-3=one leg

h-6=second leg

h^2=(h-3)^2+(h-6)^2

h^2=h^2-6h+9+h^2-12h+36

h^2=2h^2-18h+45

0=2h^2-h^2-18h+45

0=h^2-18h+45

factor

(h-15)(h-3)=0

h-15=0

h=15 cm is the length of the hypotenuse  (answer)

h-3=12 cm

h-6=9 cm

check:

15^2=12^2+9^2

225=144+81

225=225